Reputation from Kills

Killing Fel Orcs and other mobs and bosses in and around Hellfire Citadel earns Honor Hold rep (5-10 per mob, 50 per boss). Killing Shattered Hand orcs or Bleeding Hollow Necrolytes also yields 5 per kill. Mobs outside the instances only give rep through Neutral. Standard mobs in Hellfire Ramparts and Blood Furnace give rep through Friendly, with imps in the Blood Furnace giving rep through Honored. Mobs in the Shattered Halls and Heroic Mode runs of the the lower instances yield rep through Exalted.

Quests

Honor Hold quests are found in and around Honor Hold (including a couple given outside the mines just west of the Hold proper).

Repeatable Reputation Quests for Honor Hold

The PvP quest "Hellfire Fortifications" yields 150 Honor Hold rep, 4400 xp, and 3 Marks of Honor for each capture of the three towers. This can be performed once a day (and counts against the quota of daily quests). Note, however, that this means that the Horde must recapture the towers in order to repeat the quest. On Garona, that hasn't happened in some time.

Practical Notes

Apparently, the most efficient way to build rep with Honor Hold is to run Ramparts and Blood Furnace instances or to kill Shattered Hand orcs on the Path of Glory until you gain no more rep, then do all the quests, then come back at L68 and do the higher level instances. Note that many of the early quests are designed to upgrade your items to Outland-capable ones, so if you're starting off soloing, it may be more practical to do the quests first.